Stock market prices do not follow random patterns, as shown by a study analyzing stock returns from 1962 to 1985. The researchers tested this by comparing data sampled at different frequencies and found that the random walk model was strongly rejected. This rejection was consistent across various types of stock indexes and portfolios, with small stocks playing a significant role. The findings suggest that stock prices do not behave in a predictable, stationary manner, but rather follow a specific nonstationary pattern.